Mathematical Mockery in Wonderland

Some of the most iconic characters and scenes from Alice in Wonderland were missing from the original version: the Cheshire Cat, the Mad Hatter’s tea party, the trial of the Knave of Hearts and so on. The question is, why did Charles Dodgson (a.k.a. Lewis Carroll) add them later? For years, people have thought that they were references to drug use. However, Wonderland scholar Melanie Bayley, writing in New Scientist, has a different idea. She thinks that Carroll, a mathematician by day, was mocking some of the more abstract mathematical ideas of the day:

Outgunned in the specialist press, Dodgson took his mathematics to his fiction. Using a technique familiar from Euclid’s proofs, reductio ad absurdum, he picked apart the “semi-logic” of the new abstract mathematics, mocking its weakness by taking these premises to their logical conclusions, with mad results. The outcome is Alice’s Adventures in Wonderland.Take the chapter “Advice from a caterpillar”, for example. By this point, Alice has fallen down a rabbit hole and eaten a cake that has shrunk her to a height of just 3 inches. Enter the Caterpillar, smoking a hookah pipe, who shows Alice a mushroom that can restore her to her proper size. The snag, of course, is that one side of the mushroom stretches her neck, while another shrinks her torso. She must eat exactly the right balance to regain her proper size and proportions.

While some have argued that this scene, with its hookah and “magic mushroom”, is about drugs, I believe it’s actually about what Dodgson saw as the absurdity of symbolic algebra, which severed the link between algebra, arithmetic and his beloved geometry…

The madness of Wonderland, I believe, reflects Dodgson’s views on the dangers of this new symbolic algebra. Alice has moved from a rational world to a land where even numbers behave erratically.